It's obvious that r^2 = x^2+y^2... but that would only simplify the equation to:
r^2 + z^2 = 4 ... is there a better way to do this?

A better way to do what? The problem you stated was "convert the equation to cylindrical coordinates" and you did that. If you are concerned that it in not "simplified" enough, the problem did NOT say "simplify" it!